Orthogonal Frequency Division Multiplexing (OFDM) is a digital transmission technique where a given channel bandwidth is divided into subchannels and individual digital signalling tones are transmitted over each subchannel concurrently in time. This transmission scheme has been an active area of research in many systems due to its resistance to multipath fading and potential for adaptive modulation where the number of tones as well as the modulation on each tone can be varied to optimize the aggregate data rate. The fact that the Discrete Fourier Transform (DFI) or Inverse Discrete Fourier Transform (IDFT), implemented using a Fast Fourier Transform algorithm, can be used to multiplex and demultiplex the signal tones was also one of the prime contributors to a high interest in this scheme.
The use of using fast IDFT/DFT circuits is very convenient from the standpoint of system implementation. These digital circuits take as input a discrete sequence in frequency/time and generates as an output a discrete sequence in time/frequency respectively. A discretization process is needed to transform the received continuous time OFDM signal waveform to a corresponding discrete signal sequence. Conventional receivers or prior art, apply direct sampling of the continuous time OFDM waveforms to generate a corresponding discrete time sequence. This is accomplished via bandpass filtering of the received signal, followed by direct sampling by an Analog-to-Digital converter (ADC). These two operations are performed with or without first down converting the received signal from Radio Frequencies (RF) to Intemediate Frequencies (IF) and/or to Baseband Frequencies (BF). After the ADC, the a Discrete Fourier Transform is performed on the received signal samples using a Fast Fourier Transform (FFT) algorithm as shown in FIG. 1.
Apparently there is no clear justification for the detection procedures where direct sampling of the received continuous time OFDM signal is performed as part of the detection process. It is well-known that the sampling procedure is lossy with respect to information. In one or more recent papers which implicitly deals with this problem, expressions are used for the demodulated signal obtained from a received OFDM signal which look very similar to those obtained by optimum detection procedures using an infinite number of samples. However, using an infinite number of samples is not feasible in practice. Furthermore, this result does not provide a set of sufficient statistics since the signal's multiplicative time process, γ(t), is unknown and optimal filtering is not performed.
The problem of optimal signal detection has been extensively analyzed by others. In order to obtain a maximal signal-to-noise ratio (SNR) as well as the sufficient statistics such that optimality is not sacrificed, correlation receivers or matched filters, consisting of a complete set of basis functions for the received signal, must be employed at receiver's front end. If we are able to select an appropriate orthonormal basis of functions for the received OFDM signal, after optimal detection of its coordinates in the selected signal space, we are able to optimally detect the transmitted symbols carried by the OFDM signal using a Maximum Aposteriori decision rule.
Since the late 1950's, when the OFDM or Multitone transmission was invented, it was always believed that the optimal receiver is too complex to build, requiring banks of analog oscillators and banks of matched filters to de-multiplex or separate the signal tones of the received OFDM signal. For practical systems which employ 128 to 2048 signal tones, this was highly complex and costly. Thus, suboptimal receivers which employ sampling followed by FFT are considered an attractive alternative even today. The state of the art OFDM receivers today are suboptimal receivers that sample the continuous time signal and applies equalizers to remove the effects of fast fading.